doublespend – How does the double expense of bitcoin affect the omni sets?

I have a question about omni layer and bitcoin double-gas. I would be very grateful if someone answered.

Suppose I made a transaction tx_1 in the bitcoin network from the X address to the Y address and one of the outputs and its amount (546 satoshi) of bitcoin were linked to the amount of N of the omni asset (for example, Tether). So I simply sent ownership of omni asset from the X address to the Y address. Then I bounced this amount of N with another amount of satoshi, which I had had before sending Omni tied with 546 satoshi in tx_1 to this address. And then I sent this amount of omni asset to another address Z doing transaction tx_2. Then, for some reason, transaction tx_1 was canceled (double expense). And I have a question in this case omni assets will belong to the address Z or X?